Physical and Geometrical Parameters of VCBS XIII: HIP

Research in Astron. Astrophys. 2018 Vol. 18 No. 3, 000 000 http://www.raa-journal.org http://www.iop.org/journals/raa Research in Astronomy and Astrophysics Physical and Geometrical Parameters of VCBS XIII: HIP 105947 Suhail G. Masda 1,2, Mashhoor A. Al-Wardat 3 and J. M. Pathan 4 1 Physics Department, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431001, Maharashtra, India; suhail.masda@gmail.com 2 Physics Department, Hadhramout University, PO Box:50511, Mukalla, Yemen 3 Dep. of Physics and Institute of Astronomy and Space Sciences, Al al-bayt University, PO Box: 130040, Mafraq, 25113 Jordan 4 Physics Department, Maulana Azad College, Aurangabad-431001, Maharashtra, India Received 2017 Sep 24; accepted 2018 Feb 8 Abstract The perfect physical and geometrical parameters of the main-sequence close visual binary system (CVBS); HIP 105947, are explicitly presented. These parameters have been constructed conclusively using Al-Wardat s complex method for analysing CVBSs, which is a method for constructing a synthetic spectral energy distribution (SED) for the entire binary system using individual SED for each component star. Which in its turn built using Kurucz (ATLAS9) line-blanketed plane-parallel models. At the same time, the orbital parameters for the system are calculated using Tokovinin s dynamical method for constructing the best orbits of interferometric binary system. Henceforth, the mass-sum of the components, the θ and ρ residuals for the system are introduced. The combination of Al-Wardat s and Tokovinin s methods yields the estimation of the physical and geometrical parameters to their best values. The positions of the components of the system on the evolutionary tracks and isochrones are plotted and their formation and evolution are discussed. Key words: binaries: close - binaries: visual- stars: fundamental parameters-stars: individual: HIP 105947. 1 INTRODUCTION Studies of duplicity and multiplicity of stars in the Galaxy showed that their ratio reaches 50 per cent among nearby solar-type main-sequence stars Duquennoy & Mayor (1991), and 42 per cent among nearby M stars Fischer & Marcy (1992). Most of these stars are either visually close enough to each other or far away that they appear as single stars, i.e. the separation angle between the components is small, and henceforth will be called close visual binary stars (CVBSs). One of the Hipparcos mission goals was to reveal the duplicity of these stars and it reported thousands of resolved stars and their relative position measurements. At the same time and later on, several astronomical groups used special techniques like speckle-interferometry and adaptive optics with ground-based telescopes to observe these stars and to measure their relative positions and magnitude differences. The study and analysis of stellar binary systems is an extremely sensational and productive topic, especially for the estimation of stellar masses and distances which is usually derived in a considerable way from accurate analysis of synthetic spectra, keplerian motions, radial velocity curves and theoretical evolutionary tracks (Dryomova & Svechnikov 2003; Malkov et al. 2010).

2 Masda et al. Some of the physical and geometrical parameters can be estimated directly in the cases of eclipsing and spectroscopic binaries, while there is no direct way to estimate the parameters of CVBSs (Al-Wardat et al. 2017). So, Al-Wardat s complex method for analysing CVBSs (Al-Wardat et al. 2016) presents an indirect method which combines magnitude difference measurements from speckle interferometry with the system s entire spectral energy distributions from spectrophotometry along with the atmospheric modelling to estimate the physical and geometrical parameters, and it was combined with Tokovinin s method for dynamical analysis (Tokovinin 1992) to get the complete set of these parameters for the individual components of a binary system. The method has been applied with substantial success to several solar-type stars like ADS 11061, COU 1289, COU 1291, HIP 11352, HIP 11253, HIP 70973, HIP 72479, Gliese 150.2, Gliese 762.1, COU 1511, and FIN 350 (Al-Wardat 2002, 2007, 2009; Al-Wardat & Widyan 2009; Al-Wardat 2012; Al-Wardat et al. 2014b, 2016; Masda et al. 2016; Al-Wardat et al. 2017) (henceforth papers I, II, III, IV, V, VIII, X, XI and XII, respectively) and to a most rare instances like sub-giant binary systems HD 25811, HD 375 and HD 6009 Al-Wardat et al. (2014c,a); Al-Wardat (2014) (henceforth paper VI, VII and IX in this series respectively). This paper, the 13th of a series, presents the complete collection of the physical and geometrical parameters of the solar-type close visual binary system; HIP 105947 (HD 204236). As a matter of fact, HIP 105947 is known as solar neighborhood (CVBS) located at a kinematic distance of57.21±0.003 pc (17.48±1.02 mas) van Leeuwen (2007) and its measured separation is less than or equal to 0.2. The system was detected through the Hipparcos mission and the first observation was given for the 1991.25 epoch of the Hipparcos catalog ESA (1997). The first orbit of HIP 105947 was calculated by (Balega et al. 2006) depending on Monet (1977) method, their estimated mass-sum was 2.68 ± 0.58M using the old Hipparcos parallax of 17.11 ± 1.13 mas (ESA 1997). After that it was modified by (Mason et al. 2010) depending on the methods described by (Hartkopf et al. 2001), their estimated mass-sum was 2.30 ± 1.14M using the revised Hipparcos parallax of 17.48 ± 1.02 mas (van Leeuwen 2007). The last observational relative position measurement used by Mason et al. (2010) was at epoch 2009.6707. So, five new observational points from epoch 2010.4818 to epoch 2015.4974 are included in our modified orbit (Table 1). Table 1 New data of Interferometric Measurements for the HIP 105947 system. Data θ ρ (λ/ λ) Tel. References Epoch ( ) ( ) (nm) m HIP 105947 2010.4818 165.5 0.1788 562/40 3.5 (Horch et al. 2011) 2013.7363 225.8 0.0850 534 /22 4.1 (Tokovinin et al. 2014) 2014.7629 266.6 0.0726 778/132 4.2 (Tokovinin et al. 2015) 2015.4974 304.4 0.0908 543/22 4.1 (Tokovinin et al. 2016) 2015.4974 304.8 0.0952 788/132 4.1 (Tokovinin et al. 2016) Telescope aperture in meters where the observations were obtained. 2 OBSERVATIONAL DATA The entire observational spectral energy distribution (SED) for the system; HIP 105947 was taken from Al-Wardat (2003) (Figure 1), and it was used as reference for the comparison with entire synthetic SED. The observational SED (Figure 1) was obtained using a low-resolution grating (325/4 grooves/mm, 5.97 Å/px reciprocal dispersion) within the UAGS spectrograph at the 1 m (Zeiss-1000) telescope of SAO-Russia and it covers the approximate wavelength range λ 3700 to 8000 Å. Table 2 contains the fundamental data for HIP 105947. These data were taken from SIMBAD database, NASA/IPAC, Hipparcos, and Tycho Catalogues ESA (1997) and Strömgren and Table 3 shows the magnitudes difference m between the components of the system along with filters used in

Parameters of CVBS XIII: HIP 105947 3 the observation expressed in nm and reference for each value from Fourth Catalog of Interferometric Measurements of Binary Stars (INT4) 1. Table 2 The real observations data from SIMBAD database and real magnitudes and colour indices from Hipparcos, and Tycho Catalogues and Strömgren for the HIP 105947 system. Property HIP 105947 Source of data HD 204236 1 α 2000 21 h 27 m 23 s 255 SIMBAD 2 3 δ 2000 07 00 56. 95 - SAO 145409 - Sp. Typ. F8 - E(B-V) 0.10±0.003 NASA/IPAC 4 A V 0.31±0.003 - V J(Hip) 7.53 ESA (1997) B J 8.10±0.02 5 (V I) J 0.67±0.01 ESA (1997) (B V) J 0.60±0.02 - B T 8.24±0.02 5 V T 7.59±0.01 5 (u v) S 0.95±0.02 6 (v b) S 0.56±0.01 6 (b y) S 0.37±0.00 6 π Hip (mas) 17.11±1.13 ESA (1997) π Hip (mas) 17.48±1.02 Van Leeuwen (2007) Notes. 1 Right Ascention, 2 http://simbad.u-strasbg.fr/simbad/sim-fid. 3 Declination, 4 (Schlegel et al. 1998), 5 (Høg et al. 2000), 6 (Hauck & Mermilliod 1998), 3 METHOD AND ANALYSIS 3.1 HIP 105947 Entire visual magnitude of the binary (m v (V J )) and magnitude difference between its components ( m) are the start keys of applying Al-Wardat s complex method for analysing CVBSs. Together, they led to the determination of the apparent magnitudes of the individual components of the system using the following simple relationships: m A v = m v +2.5log(1+10 0.4 m ), (1) m B v = m A v + m, (2) and their errors follow using the following equations: σ 2 m = 1 A σ2 v m v +( 1+10 +0.4 m)2 σ m, 2 (3) σ 2 m B v = σ2 m A v +σ2 m (4) For the system HIP 105947, the mean speckle-interferometric magnitude difference was taken as 1 m.53±0.07, which is the average of all m measurements under different speckle filters for V-band filters (534-562) nm with different band widths (see Table 3), as the closest filters tov J. 1 http://www.usno.navy.mil/usno/astrometry/optical-ir-prod/wds/int4

4 Masda et al. Table 3 Magnitude difference between the components of the HIP 105947 system and available errors, along with filters used to obtain the observations. m σ m Filter (λ/ λ) Ref. (mag) ( nm) 1.17 0.60 V Hip : 550/40 1 1.50 0.04 545/30 2 1.40 0.02 545/30 3 1.29 0.05 850/75 3 1.31 0.06 600/30 3 1.47 0.03 545/30 4 1.56 * 550/40 5 1.56 * 550/40 6 2.00 * 551/22 7 1.40 * 657/05 7 1.50 * 551/22 7 1.50 * 788/132 8 1.37 * 692/40 9 1.44 * 562/40 9 1.90 * 534/22 10 1.10 * 788/132 11 1.30 * 543/22 12 1.50 * 788/132 12 The errors are not given in Fourth Catalog of Interferometric Measurements of Binary Stars (INT4). 1 ESA (1997), 2 Pluzhnik (2005) 3 (Balega et al. 2006), 4 (Balega et al. 2007), 5 (Horch et al. 2008), 6 (Horch et al. 2010), 7 (Tokovinin et al. 2010b), 8 (Tokovinin et al. 2010a), 9 (Horch et al. 2011), 10 (Tokovinin et al. 2014), 11 (Tokovinin et al. 2015), 12 (Tokovinin et al. 2016). This value was implemented concurrently with the entire visual magnitude m v = 7 m.53 of the system (Table 2) in Equations 1 & 2, and resulted in calculating the individual apparent magnitudes of the components of the system as m A v = 7 m.77 ± 0.01 and m B v = 9 m.30 ± 0.07 for the primary and secondary components of the system, respectively. Using the updated Hipparcos parallax of d = 57.21 ± 0.003 pc van Leeuwen (2007), with the following relation: M V m v = 5 5log(d) A V, (5) the absolute magnitudes along with their errors follow as:m A V = 3m.98±0.13 andm B V = 5m.51±0.14. Note that the interstellar extinction can be neglected (A V 0) because the system is a nearby one. The errors of the absolute magnitudes were calculated using the following relation: σ 2 M V = σ2 m v +( loge 0.2π Hip ) 2 σ 2 π Hip ; * = A,B. (6) where σ m v are the errors of the apparent magnitudes of the A and B components in Equations 3 & 4. Hence, depending on the estimated preliminary absolute magnitudes, the preliminary values of the effective temperature and gravity acceleration for each component were taken from the Tables of Lang (1992) and Gray (2005) as follows: T eff = 6200K, log g = 4.31 for the primary component and T eff = 5490K, log g = 4.47 for the secondary component. Note that for solar-type stars, these parameters are related to other parameters according to the following equations: log R R = M bol M bol 5 2log T eff T, (7) logg = log M M 2log R R +logg. (8)

Parameters of CVBS XIII: HIP 105947 5 wheret = 5777K,M bol = 4m.75 and logg = 4.44.M bol = M V +BC;BC indicates the bolometric correction. Now, we have the preliminary input parameters to build model atmospheres for each individual component of the system, and to do so we use ATLAS9 line-blanketed model atmospheres of Kurucz (1994). In order to build a synthetic SED of a star from its model atmospheres, we need information about its distance d and radius R. The first parameter d was taken from the updated Hipparcos parallax (d = 57.21 ± 0.003 pc) as a postulate value with its error, while the second parameter is subject to change within the values of the observational data like entire SED, magnitudes and colour indices. The method make use of the entire observational SED as a reference guide for the best-fitted entire synthetic SED, in an iterated way. The entire synthetic SED of the binary system, which is connected to the energy flux of the individual components A and B located at a distance d (pc) from the Earth, is calculated using the following equation: This equation can be written as F λ d 2 = H A λ R 2 A +H B λ R 2 B, (9) F λ = ( R A d )2 (H A λ +H B λ ( R B R A ) 2 ), (10) where F λ is the flux for the entire synthetic SED of the entire binary system at the Earth, H A λ and HB λ are the fluxes of the primary and secondary star, in units of ergs cm 2 s 1 Å 1, while R A and R B are the radii of the primary and secondary components of the binary system in solar units. Many attempts were carried out tell the best-fit between the synthetic and observational SEDs was achieved. Hence, the physical and geometrical parameters of the best-fitted synthetic SED represent adequately enough the parameters of the system s components within the error limits of the observational SED. It is very important to mention here that the values of the radii are totally reliant on Hipparcos parallax measurements precision (see Equation 10), which in some cases is distorted by the orbital motion of the components of such systems as pointed out by Shatskii & Tokovinin (1998). The parameters which led to the best-fit were as follows (Figure 1): T A eff = 6230±80K,T B eff = 5470±80K, logg A = 4.30±0.07,logg B = 4.45±0.08 R A = 1.443±0.06R,R B = 0.989±0.05R The errors of the radii were estimated from the method and double-checked using the following equation: σ R ±R ( σ M bol 5loge )2 +4( σ T eff ) T 2 (11) eff The individual stellar luminosities and bolometric magnitudes of the system follow as: L A = 2.816±0.30L,L B = 0.786±0.10L,M A bol = 3m.63±0.08 andm B bol = 5m.01±0.09, respectively. Figures 3&5 show the positions of the components on the Hertzsprung-Russell (H-R) evolutionary tracks and isochrones of the binary system. Depending on that, the masses of the components can be estimated as: M A = 1.21±0.21M, M B = 0.89±0.15M with spectral types F8 for the primary and G7.5 for the secondary and the age of the system as t T 2.75±0.06 Gyr.

6 Masda et al. Log F (erg.cm -2.s -1.Å -1 ) -11.4-11.6-11.8-12.0-12.2-12.4-12.6-12.8 HIP 105947 A HIP 105947 B Entire flux HIP 105947 Entire flux (Observational spectrum) Entire flux (Synthetic spectrum) 4000 4500 5000 5500 6000 6500 7000 7500 Wavelength (Å) Fig. 1 The entire synthetic SED of the system HIP 105947 (built using parameters given in Table 6 like T eff, logg, R and Parallax) against the observational one, the Figure also shows the synthetic SED for each component. 4 SYNTHETIC PHOTOMETRY Notwithstanding the significance and easiness of the direct comparison between synthetic and observed spectra in determining the best-fit, there is another powerful and quantitative technique which examines this fitting, it is the synthetic photometry. It helps us to calculate the apparent magnitudes and colour indices of the entire and individual SEDs in any photometrical system, and enables us to compare the synthetic photometry with the observational one. The apparent magnitude for a specific photometric filter can be done using the following equation (Maíz Apellániz 2007; Al-Wardat 2012): m p [F λ,s (λ)] = 2.5log Pp (λ)f λ,s (λ)λdλ Pp (λ)f λ,r (λ)λdλ +ZP p (12) where m p is the synthetic magnitude of the passband p, P p (λ) is the dimensionless sensitivity function of the passband p, F λ,s (λ) is the synthetic SED of the object and F λ,r (λ) is the SED of the reference star (Vega). Zero points (ZP p ) from Maíz Apellániz (2007) are adopted. The calculated magnitudes and colour indices of the individual components and entire synthetic SEDs for the system, in different photometrical systems (Johnson:U,B,V,R,U B,B V,V R; Strömgren: u,v,b,y,u v,v b, b y and Tycho: B T, V T,B T V T ), are listed in Table 4. Table 8 shows a good agreement between synthetic and observational magnitudes and colour indices, which reflects well on the best-fit between the synthetic and observational SED and hence the reliability of Al-Wardat s complex method in estimating the physical and geometrical parameters of CVBS.

Parameters of CVBS XIII: HIP 105947 7 Table 4 Magnitudes and colour indices of the entire synthetic spectrum and individual components of HIP 105947. Sys. Filter Entire Synth. HIP 105947 HIP 105947 σ = ±0.03 A B Joh- U 8.24 8.39 10.47 Cou. B 8.13 8.32 10.10 V 7.53 7.77 9.30 R 7.20 7.46 8.88 U B 0.11 0.07 0.37 B V 0.60 0.55 0.79 V R 0.33 0.30 0.42 Ström. u 9.40 9.56 11.61 v 8.45 8.63 10.52 b 7.87 8.08 9.73 y 7.50 7.74 9.27 u v 0.95 0.93 1.09 v b 0.59 0.55 0.79 b y 0.37 0.34 0.47 Tycho B T 8.27 8.45 10.31 V T 7.60 7.83 9.39 B T V T 0.67 0.62 0.92 5 ORBITS AND MASSES 5.1 Orbits The orbital solution also plays a vital role in calculating stellar masses. This solution involves the orbital period P (in years); the eccentricity e; the semi-major axis a (in arcsec); the inclinationi(in degree); the argument of periastronω (in degree); the position angle of nodesω(in degree); and the time of primary minimum T 0 (in years). In order to derive the orbital parameters for the system, we followed Tokovinin s dynamical method Tokovinin (1992). The method performs a least-squares adjustment to all available relative position measurements and radial velocity (once available), with weights inversely proportional to the square of their standard errors. The initial determinations of the orbital parameters were carried out based on four parameters (P, T, e and a). These parameters are intrinsic keys in applying the least-squares method and then to get the rest of the orbital parameters. The results of the dynamical analysis and orbital solutions of HIP 105947 are listed in Table 7, and the orbit is shown in Figure 2. 5.2 Masses As formerly mentioned that the mass is an intrinsically crucial parameter because the mass of the star determines its present and future, i.e. the birth, life and death of a star. As a result, using the estimated orbital solutions for the system in Table 7, period and semi-major axis, combined with the revised Hipparcos parallax (van Leeuwen 2007) for the system, led us to calculate the total mass along with its error for the system according to Kepler s third law: M Tot. = M A +M B = ( a3 π 3 P 2) M (13) σ M M = 9( σ π π )2 +9( σ a a )2 +4( σ P P )2 (14)

8 Masda et al. Table 5 Relative position measurements, residuals θ and ρ (Our work) and rms for HIP 105947, which are used to build the orbit of the system. θ and ρ are taken from the Fourth Catalog of Interferometric Measurements of Binary Stars. Epoch θ ρ Ref. θ ρ ( ) ( ) ( ) ( ) 1991.25 171.64 0.1266 1-11.1-0.008 1997.7201 177.6 0.151 2 - - 1998.7796 219.2 0.108 3 5.7-0.001 1999.7468 242.2 0.110 3 0.3-0.002 2000.8643 84.6 0.127 4 0.1-0.000 2001.7523 98.5 0.144 4 0.3-0.000 2001.7523 98.5 0.143 4 0.3-0.001 2002.7986 112.2 0.170 5 1.6 0.005 2002.7987 110.9 0.168 5 0.3 0.003 2002.799 110.0 0.163 2-0.6-0.002 2002.799 110.7 0.163 2 0.1-0.002 2004.815 127.5 0.195 2-0.2-0.004 2004.8152 127.5 0.195 6-0.3-0.004 2006.4436 138.2 0.211 5-0.2-0.003 2006.5254 139.0 0.226 7 0.1 0.011 2006.6870 140.7 0.215 5 0.8-0.000 2008.4613 151.5 0.214 8 0.7 0.003 2008.5430 151.5 0.2102 9 0.2-0.001 2008.7669 152.6 0.2084 9-0.1-0.000 2008.7669 152.5 0.2073 9-0.2-0.001 2009.6706 159.0 0.1951 10 0.0-0.001 2009.6707 159.0 0.195 11 0.0-0.001 2010.4818 165.5 0.1788 12 0.1-0.001 2013.7363 225.8 0.0850 13-2.5 0.003 2014.7629 266.6 0.0726 14-10.1-0.006 2015.4974 304.4 0.0908 15-0.4-0.004 2015.4974 304.8 0.0952 15 0.0 0.001 rms 0.60 0.0015 Notes: It was neglected in our orbits (Mason et al. 1999), These points were modified by180 to achieve consistency with nearby points and New observations in our orbit. 1 ESA (1997), 2 (Balega et al. 2006), 3 (Balega et al. 2002a), 4 (Balega et al. 2002b), 5 (Balega et al. 2013), 6 (Balega et al. 2007), 7 (Horch et al. 2008), 8 (Horch et al. 2010), 9 (Tokovinin et al. 2010b), 10 (Tokovinin et al. 2010a), 11 (Mason et al. 2010), 12 (Horch et al. 2011), 13 (Tokovinin et al. 2014), 14 (Tokovinin et al. 2015). where P is the orbital period (in years), M A and M B are the masses (in solar mass), a and π are the semi-major axis and the Hipparcos parallax (both in arcsec), respectively. Using Equation 13, we obtained the mass-sum for HIP 105947 as 2.06±0.36M. Comparing this result with the estimated masses using Al-Wardat s method by plotting the positions of the components on the H-R diagram (see Table 6 and Figure 3), we find a good coincidence between them. This means that the analysis in both methods as well as combination of two methods together was successful, and consequently obtained the precise physical and geometrical parameters of the studied CVBS. 6 RESULTS AND DISCUSSION The results of combining Al-Wardat s complex method for analysing CVBSs with Tokovinin s dynamical method in analysing the CVBS, HIP 105947, are explicitly presented. Table 6 shows the final physical and geometrical parameters of the individual components for the system. Figure 1 shows the best-fitting between the entire synthetic and observational SED along with the SED for each individual component presented for the first time.

Parameters of CVBS XIII: HIP 105947 9 Table 6 The estimated parameters of the individual components of HIP 105947. HIP 105947 Parameters Units HIP 105947 A HIP 105947 B T eff ±σ Teff [ K ] 6230±80 5470±80 R±σ R [R ] 1.443±0.06 0.989±0.05 logg ±σ logg [cgs] 4.30±0.07 4.45±0.08 L ±σ L [L ] 2.816±0.30 0.786±0.10 M bol ± σ Mbol [mag] 3.63±0.08 5.01±0.09 M V ± σ MV [mag] 3.98±0.13 5.51±0.14 M a ± σ M [M ] 1.21±0.21 0.89±0.15 Sp. Type b F8 G7.5 Parallax c [mas] 17.48±1.02 (M A +M B) d [M ] 2.06±0.36 Age e [Gyr] 2.75±0.06 a Depending on the evolutionary tracks of masses ( 0.8, 0.9,..., 1.3 M ) of (Girardi et al. 2000b) (Figure 3). b By using the tables of Lang (1992); Gray (2005) and depending onm V S P relation. c The revised Hipprcoas parallax of 57.21±0.003 pc for HIP 105947 van Leeuwen (2007). d Depending on the orbital solutions and Tokovinin s method Tokovinin (1992). e Depending on the the isochrones for low- and intermediate-mass stars of different metallicities of (Girardi et al. 2000a) (Figures 4& 5). Table 7 Orbital parameters solutions and total masses formerly published for the HIP 105947 system, for comparison with this work. System HIP 105947 Parameters Units (Balega et al. 2006) (Mason et al. 2010) This work P ±σ P [yr] 18.79±0.57 20.3±4.9 20.78±0.06 T 0 ± σ T0 [yr] 1993.96±0.40 1994.7±2.6 1994.94±0.06 e ±σ e - 0.354±0.010 0.37±0.25 0.347±0.001 a ±σ a [arcsec] 0.168±0.003 0.171±0.018 0.168±0.0004 i ± σ i [deg] 57.1±2.1 54.5±3.9 51.78±0.27 ω ±σ ω [deg] 149.1±1.5 140.0±14.0 148.00±0.72 Ω ±σ Ω [deg] 129.7±6.4 154.0±12.0 152.41±0.30 M T± σ M [M ] 2.68±0.58 2.30±2.2 2.06±0.36 π Hip ±σ πhip [mas] 17.11±1.13 a 17.48±1.02 b 17.48±1.02 b a The old Hipprcoas parallax ESA (1997), b The revised Hipprcoas parallax van Leeuwen (2007) Table 8 shows a very good coincidence between the synthetic magnitudes and colour indices with the observational ones for the system. Without a doubt, this gives lucid and powerful indication for the reliability of the estimated physical and geometrical parameters of the individual components for the system as shown in Table 6. Table 7 summarizes the ultimate results of our orbital solutions with former studies for the system, and the orbit is plotted in Figure 2. In addition to that, Table 5 lists the residuals θ and ρ and rms for HIP 105947. The results of the orbital solutions show a slight modifications in the orbital parameters. The rms for our orbital solutions are0.60 and 0.0015 for HIP 105947. The stellar masses for the system were calculated using two independent methods; Al-Warda s complex method for analysing CVBSs and Tokovinin s dynamical method for orbital solutions of binary stars. The former gives 2.10±0.19M for HIP 105947 (see Figure 3& Table 6), while the latter gives 2.06±0.36M for HIP 105947 (see Table 7). Both methods used the revised Hipparcos parallax van Leeuwen (2007).

10 Masda et al. 0.15 0.10 0.05 N E 1998.78 1999.747 2015.497 (2 points) y (arcsec) 0.00-0.05-0.10-0.15-0.20 2000.864 2001.752 (2 points) 2002 (4 points) 2004.815 (2 points) 2008 (4 points) 2006 (3 points) 2010.482 2009.671 (2 points) 2014.763 2013.736 1991.25 (Hipparcos point) -0.25-0.20-0.15-0.10-0.05 0.00 0.05 0.10 0.15 x (arcsec) Fig. 2 The relative orbit of the binary system HIP 105947 constructed using the relative position measurements from the Fourth Catalog of Interferometric Measurements of Binary Stars. The origin point represents the position of the primary component. A fast look and comparison with old orbital parameters for the system shows that for HIP 105947, Balega et al. (2006) used the old Hipparcos parallax ESA (1997) to estimate the masses, whereas Mason et al. (2010) used the revised Hipparcos parallax but their eccentricity e and sem-major axis a were to a certain extent high unlike Balega et al. (2006) and ours. Of course, these discrepancies are due to the availability of new observational measurements given in the Fourth Catalog of Interferometric Measurements of Binary Stars. Table 4 lists the results of the synthetic photometry of the entire system and individual components of HIP 105947, in different photometrical systems (Johnson: U, B, V, R, U B, B V, V R; Strömgren: u,v,b,y,u v,v b, b y and Tycho: B T, V T,B T V T ). The positions of the individual components of the system are shown on the evolutionary tracks of (Girardi et al. 2000b) (Figure 3). The Figure shows that all components belong to the main sequence stars but the primary and secondary components of the system HIP 105947 are totally similar to the primary and secondary components of the double-lined spectroscopic binary system HD 22128 Folsom et al. (2013), which are well-known as zero-age main-sequence. Therefore, this led us to a broad suggestion that both components of the system HIP 105947 are zero-age main-sequence stars. The analysis

Parameters of CVBS XIII: HIP 105947 11 Table 8 Comparison between the observational and synthetic magnitudes and colours indices for both systems. HIP 105947 Filter Observed a Synthetic b (This work) (mag) (mag) V J 7.53 7.53±0.03 B J 8.10±0.02 8.13±0.03 B T 8.24±0.02 8.27±0.03 V T 7.59±0.01 7.60±0.03 (B V) J 0.60±0.02 0.60±0.03 (u v) S 0.95±0.015 0.95±0.03 (v b) S 0.56±0.003 0.59±0.03 (b y) S 0.37±0.000 0.37±0.03 m 1.53 c ±0.07 1.53 d ±0.05 Notes. a A real observations (see Table 2) b Synthetic work of the HIP 105947 system by using Interactive Data Language (IDL) program (see Table 4) c As the average of all m measurements under the speckle filters V-band only 534-562 nm (see Table 3) d The magnitude difference between the A and B component ( m = VJ B -VJ A ) (see Table 4) 0.8 0.6 0.4 1.3M Log (L/L ) 0.2 0.0 1.2M 1.1M -0.2-0.4 HIP 105947 A HIP 105947 B ZAMS 1M 0.9M 3.82 3.80 3.78 3.76 3.74 3.72 3.70 Log T eff Fig. 3 The evolutionary tracks of both components of HIP 105947 on the H-R diagram of masses ( 0.8, 0.9,..., 1.3 M ). The evolutionary tracks were taken from Girardi et al. (2000b). of the system HIP 105947 shows that both of its components are of age around 2.75 ± 0.06 Gyr and solar composition [Z = 0.019, Y = 0.273] (Girardi et al. 2000a) (see Figures 4& 5).

12 Masda et al. 0.6 0.4 0.2 Log L/L 0.0-0.2-0.4-0.6 HIP 105947 A HIP 105947 B 0.001 0.0004 0.03 0.019 0.004 0.008-0.8 3.80 3.79 3.78 3.77 3.76 3.75 3.74 3.73 3.72 Log T eff Fig. 4 The isochrones for both components of HIP 105947 on the H-R diagram for low- and intermediate-mass stars of different metallicities. The isochrones were taken from Girardi et al. (2000a). 7 CONCLUSIONS Using Al-Wardat s method for analysing CVBSs which employs Kurucz ATLAS9 line-blanketed planeparallel model atmospheres in constructing the entire and individual synthetic SEDs for a binary system, along with Tokovinin s dynamical method for orbital solutions of binary stars, we were able to estimate the complete set of physical and geometrical parameters of the Main-Sequence CVBS, HIP 105947. The calculated entire and individual synthetic magnitudes and colour indices of the system for different photometrical systems such as Johnson-Cousin UBV R, Strömgren uvby and Tycho BV are introduced. Revised orbits and orbital parameters for the system are introduced and compared with previous studies. The ideal positions of the components of the system are shown with a broad way on the evolutionary tracks and isochrones. The spectral types of the components of HIP 105947 are catalogued as F8 and G7.5 for the primary and secondary components of the system, respectively with an age of 2.75 ± 0.06 Gyr. Depending on the estimated physical and geometrical parameters of the system, the fragmentation process for the formation of such system is the most likely one, where the rotating disc around an incipient central protostar in case of continuing infall and the hierarchical fragmentation during rotational collapse are the main mechanisms in producing binaries and multiple systems, as pointed out by Bonnell (1994) and Zinnecker & Mathieu (2001). Acknowledgements This research has made use of SAO/NASA, SIMBAD database, Fourth Catalog of Interferometric Measurements of Binary Stars, IPAC data systems, ORBIT code and CHORIZOS

Parameters of CVBS XIII: HIP 105947 13 0.6 0.5 0.4 1.78 2.24 2.51 2.82 2 3.16 Gy Log L/L 0.3 0.2 0.1 0.0-0.1 1.59 1.41 1.23 1.22 1 Gy HIP 105947 A HIP 105947 B 3.81 3.80 3.79 3.78 3.77 3.76 3.75 3.74 3.73 Log T eff Fig. 5 The isochrones for both components of HIP 105947 on the H-R diagram for low- and intermediate-mass: from 0.15 to 7M, and for the compositions [Z=0.019, Y=0.273] stars of different metallicities. The isochrones were taken from Girardi et al. (2000a). code of photometric and spectrophotometric data analysis. Suhail Masda would like to thank Human Development Fund for the scholarship and Hadhramout University in Yemen for perpetual support. References Al-Wardat, M. A. 2002, Bull. Special Astrophys. Obs., 53, 51 Al-Wardat, M. A. 2003, Bulletin of the Special Astrophysics Observatory, 55, 18 Al-Wardat, M. A. 2007, Astronomische Nachrichten, 328, 63 Al-Wardat, M. A. 2009, Astronomische Nachrichten, 330, 385 Al-Wardat, M. A. 2012, PASA, 29, 523 Al-Wardat, M. A. 2014, Astrophysical Bulletin, 69, 454 Al-Wardat, M. A., Balega, Y. Y., Leushin, V. V., et al. 2014a, Astrophysical Bulletin, 69, 58 Al-Wardat, M. A., Balega, Y. Y., Leushin, V. V., et al. 2014b, Astrophysical Bulletin, 69, 198 Al-Wardat, M. A., Docobo, J. A., Abushattal, A. A., & Campo, P. P. 2017, Astrophysical Bulletin, 72, 24 Al-Wardat, M. A., El-Mahameed, M. H., Yusuf, N. A., Khasawneh, A. M., & Masda, S. G. 2016, Research in Astronomy and Astrophysics, 16, 166 Al-Wardat, M. A., & Widyan, H. 2009, Astrophysical Bulletin, 64, 365 Al-Wardat, M. A., Widyan, H. S., & Al-thyabat, A. 2014c, PASA, 31, e005 Balega, I. I., Balega, Y. Y., Gasanova, L. T., et al. 2013, Astrophysical Bulletin, 68, 53 Balega, I. I., Balega, Y. Y., Hofmann, K.-H., et al. 2002a, A&A, 385, 87 Balega, I. I., Balega, Y. Y., Hofmann, K.-H., et al. 2006, A&A, 448, 703 Balega, I. I., Balega, Y. Y., Maksimov, A. F., et al. 2007, Astrophysical Bulletin, 62, 339

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